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Simplify the expression fraction with numerator of the square root of negative four and denominator of the quantity three plus i minus the quantity two plus three times i. quantity eight plus two times i divided by seventeen quantity negative four plus two times i divided by five quantity four plus ten times I divided by twenty nine quantity eight plus ten times I divided by forty one

Respuesta :

Does it look like this: [tex] \frac{ \sqrt{-4} }{(3+i)-(2+3i)} = \frac{-2i}{1-2i} [/tex] or [tex] \frac{2i}{2i-1} [/tex]

Do you need the others?
[tex] \frac{-4+2i}{-5} = \frac{4-2i}{5} [/tex]

Answer:

[tex]\frac{-4+2i}{5}[/tex]  

Step-by-step explanation:

[tex]\frac{\sqrt{-4}}{(3+i)-(2+3i)}[/tex]

simplify the denominator

[tex]\frac{\sqrt{-4}}{1-2i}[/tex]

square root (-4) is +2i , because the value of square root (-1) is 'i'

[tex]\frac{+2i}{1-2i}[/tex]                    

multiply top and bottom by its conjugate 1+2i

[tex]\frac{2i(1+2i)}{(1-2i)(1+2i)}[/tex]  

[tex]\frac{2i+4i^2}{1+2i-2i-4i^2}[/tex]  

The value of i^2 =-1

[tex]\frac{2i+4(-1)}{1+2i-2i-4(-1)}[/tex]  

[tex]\frac{2i-4}{5}[/tex]  

[tex]\frac{-4+2i}{5}[/tex]  




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